Clustering and ensembles inequivalence in the / 4 and / 6 mean-field Hamiltonian models
Résumé
We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second (/ 4) or both a second and a first-order phase transition separated by tricritical points (/ 6). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the / 4-model. Moreover, long-lived out-of-equilibrium states appear close to the second-order phase transition when starting with ''water-bag'' initial conditions, in analogy with what has been found for the Hamiltonian mean-field model. The microcanonical simulations of the / 6-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.
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